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GMModelInterfaces Interface CATICGMLocalAnalysis2D

Usage: an implementation of this interface is supplied and you must use it as is. You should not reimplement it.

interface CATICGMLocalAnalysis2D

Class defining the local analysis on a point of a CATSurface.

It performs curvature, torsion, main normal and binormal on a point of a CATSurface. This class is not streamable. The point where the analysis is done can be changed by .

Method Index

o GetCurvatureAlongDirection(double&,double&): Returns the curvature along a direction of the surface.
o GetFirstFundamentalForm(double&,double&,double&): Retrieves the first fondamental form at the point of this CATICGMLocalAnalysis2D.
o GetGaussianCurvature(): Returns the gaussian curvature at the point of this CATICGMLocalAnalysis2D.
o GetMeanCurvature(): Returns the mean curvature at the point of this CATICGMLocalAnalysis2D.
o GetMinMaxCurvature(double&,double&): Returns the min and max curvatures at the point of this CATICGMLocalAnalysis2D.
o GetMinMaxCurvaturesAndDirections(double&,double&,CATMathVector2D&,CATMathVector2D&,CATMathVector&,CATMathVector&): Returns the min and max curvatures at the point of this CATICGMLocalAnalysis2D, along with the associated principal curvature directions.
o GetSecondFundamentalForm(double&,double&,double&): Retrieves the second fondamental form at the point of this CATICGMLocalAnalysis2D.
o IsARegularParam(): Tests whether the point of this CATICGMLocalAnalysis2D is regular.
o ProjectVector(CATMathVector&,double&,double&): Returns the 2D coordinates of the projection of the 3d vector iVector on the surface.
o SetParam(CATSurParam&): Modifies the point where this CATLocalAnalysis2D is performed.

Methods

o GetCurvatureAlongDirection

public virtual GetCurvatureAlongDirection(	const	`iX`,
	const	`iY`)

Returns the curvature along a direction of the surface.

Parameters:

iX: The first coordinate of the direction in the space of the surface.
iY: The second coordinate of the direction in the space of the surface.

Returns:

The curvature. C(iX,iY) = (L.iX^2+2M.iX.iY+N.iY^2) / (E.iX^2+2F.iX.iY+G.iY^2), where L,M,N are the coordinates of the second fundamental form and E, F, G the coordinates of the first fundamental form

o GetFirstFundamentalForm

public virtual GetFirstFundamentalForm(		`ioE`,
		`ioF`,
		`ioG`)

Retrieves the first fondamental form at the point of this CATICGMLocalAnalysis2D.

Parameters:

ioE: The first coordinate: ioE = FirstDerivU.Norm() ^ 2, where FirstDerivU is the first derivative with regards to the first parameter.
ioF: The second coordinate: ioF = FirstDerivU * FirstDerivV, where * is the dot product.
ioE: The third coordinate: ioG = FirstDerivV.Norm() ^ 2, where FirstDerivV is the first derivative with regards to the second parameter.

o GetGaussianCurvature

public virtual GetGaussianCurvature(

)

Returns the gaussian curvature at the point of this CATICGMLocalAnalysis2D.

Returns:: The Gaussian curvature = Cmin*Cmax, where Cmin is the minium curvature and Cmax the maximum curvature at the point of this analysis.

o GetMeanCurvature

public virtual GetMeanCurvature(

)

Returns the mean curvature at the point of this CATICGMLocalAnalysis2D.

Returns:: The mean curvature: = 0.5*(Cmin+Cmax) .

o GetMinMaxCurvature

public virtual GetMinMaxCurvature(		`ioCmin`,
		`ioCmax`)

Returns the min and max curvatures at the point of this CATICGMLocalAnalysis2D.

Parameters:

ioCmin: The minimum curvature.
ioCmax: The maximum curvature: ioCmin < ioCmax.

o GetMinMaxCurvaturesAndDirections

public virtual GetMinMaxCurvaturesAndDirections(		`ioCmin`,
		`ioCmax`,
		`ioDirMin2D`,
		`ioDirMax2D`,
		`ioDirMin3D`,
		`ioDirMax3D`)

Returns the min and max curvatures at the point of this CATICGMLocalAnalysis2D, along with the associated principal curvature directions. The returned 3d and 2d vectors represent directions: no assumption can be made regarding the orientation of the vectors. Likewise, the directions are unspecified at umbilical points (when min curvature = max curvature).

Parameters:

ioCmin: The minimum curvature.
ioCmax: The maximum curvature: ioCmin < ioCmax.
ioDirMin2D: The principal curvature direction associated to the minimal curvature, expressed as a linear combination of the partial derivatives.
ioDirMax2D: The principal curvature direction associated to the maximal curvature. expressed as a linear combination of the partial derivatives.
ioDirMin3D: The principal curvature direction associated to the minimal curvature, expressed in 3D.
ioDirMax3D: The principal curvature direction associated to the maximal curvature, expressed in 3D.

o GetSecondFundamentalForm

public virtual GetSecondFundamentalForm(		`ioL`,
		`ioM`,
		`ioN`)

Retrieves the second fondamental form at the point of this CATICGMLocalAnalysis2D.
Let H = (FirstDerivU ^ FirstDerivV) / (FirstDerivU ^ FirstDerivV).Norm().

Parameters:

ioL: The first coordinate: ioL = SecondDerivU2 * H, where SecondDerivU2 is the second derivative with regards to the first parameter and * the dot product.
ioM: The second coordinate: ioM = SecondDerivUV * H, where SecondDerivUV is the second derivative with regards to the first parameter and second parameters, and * the dot product.
ioN: The third coordinate: ioN = SecondDerivU2 * H, where SecondDerivV2 is the second derivative with regards to the second parameter and * the dot product.

o IsARegularParam

public virtual IsARegularParam(

)

Tests whether the point of this CATICGMLocalAnalysis2D is regular.
A point is non regular when the partial derivative of one of its coordinate is null.

Returns:

The result of the test.
Legal values:

0: if it is not regular
1: if it is regular

o ProjectVector

public virtual ProjectVector(		`iVector`,
		`ioX`,
		`ioY`)

Returns the 2D coordinates of the projection of the 3d vector iVector on the surface.
These coordinates are such that: iVector = ioX*FirstDerivU + ioY*FirstDerivV, where FirstDerivU and FirstDerivV are the first derivatives with respect to the first and second surface parameters, and * is the dot product.

Parameters:

ioX: The coordinate along the first derivative with regards to the first surface parameter.
ioY: The coordinate along the first derivative with regards to the second surface parameter.

Returns:

The regularity of the point.

0: if it is not regular (ioX and ioY are not calculated)
1: if it is regular

o SetParam

public virtual SetParam( const iNewParamToAnalyze)

Modifies the point where this CATLocalAnalysis2D is performed.
The analysis is automatically done.

Parameters:

iNewParamToAnalyze: The parameter of the new point to analyze.

This object is included in the file: CATICGMLocalAnalysis2D.h
If needed, your Imakefile.mk should include the module: CATGMModelInterfaces